US Patent 7587063 Asymmetric subspace watermarking

According to an asymmetric watermarking technology, which is particularly resistant to projection attack, an original image is analyzed to obtain its watermarking space. The watermarking space is then divided to obtain two orthogonal subspaces g and h. An embedding key G, which is a matrix and which columns form bases of subspace g, is selected and a matrix H, HTG=0 is calculated. Columns of matrix H form bases of subspace h. A detecting key D, which equals the sum D= GT=BHT, wherein B is a matrix, is calculated, and a watermark w is obtained and embedded into the original image φ0 to obtain a watermarked image φw=φ0+Gw, wherein Dφ0=m0 is not a 0 vector.